Waves and Particles

1. Waves and Particles • Topics • Light as a wave; • Light as a particle; • Particle-wave duality; • The wave-like nature of matter; • Motivation • Learn about the particle-wave duality of matter and energy. • Learn how physics can blow your brain.

2. Light as a Wave • Characteristics of typical waves • Waves transmit energy; • Waves move; • Waves are diffuse, without well defined edges; • Waves travel through a medium; • Waves may be longitudinal or transverse; • Objects can move slower, faster, or the same speed as waves. • Examples of light being wavelike • Interference; • Antireflective coatings.

3. Maxwell’s Equations • Gauss’s Law • Gauss’s Law of Magnetism • Faraday’s Law of Induction • Ampère’s Law • Maxwell’s correction • Maxwell added the final term in Ampere’s Law, showing that electrical fields and magnetic fields are related. A consequence of that term is that pulses in these fields travel at a speed “s”: • Electricity and magnetism are united, and to optics as well!!!!

4. The Aether • Wave Speed • Different types of waves travel at different speeds, -- Seismic waves: P (5000 m/s), S (3000 m/s) • -- Light and sound waves (hence thunder delays) • The medium affects the wave speed: • -- vsound = 343 m/s (air), 1484 m/s(water), 5120 m/s (steel) • The nature of the luminiferous aether • A medium for light (aether) was proposed in 1678. • Aether must be very stiff to account for light’s high speed. • Michelson interferometer could not detect it in 1887. • We will wait for Einstein (1905) to understand why.

5. Light as a Particle • Photoelectric effect • In 1887, Hertz noted that high energy light (ultraviolet) on polished metal can knock off electrons. • In 1905, Einstein explained this “photo-electric effect” as discrete light particles (photons) knocking the electrons out of the metal surface. This earned Einstein the Nobel Prize in 1921.

6. Particle-Wave Duality • Wave or Particle? • Low energy light (radio waves, microwaves) act very wave-like. • High-energy light (X-ray, gamma rays) act very particle-like. • In general, photons can act either like waves OR particles. Light is BOTH wave-like and particle-like. • This is called particle-wave duality. • Example: Single-slit vs. double-slit diffraction patterns. • Weirder still, we will see that even matter is both wave-like and particle-like—electron diffraction patterns can be generated.

7. Optics and Matter: Quantum physics • The three postulates of the Bohr atom • Electrons occur in stable orbits around a nucleus; each orbit has an energy. • An electron can move from one energy level to another; the change in energy is associated with a photon of equivalent energy being emitted or absorbed. • The orbits can have only certain specific energies (these energy levels are said to be quantized).

8. Electrons as Waves? • Electrons are wave-like! The de Broglie wavelength; • λ=h/p • (~ 0.4 nm, the size of atoms.) • Bohr’s electron orbits are set by the sizes needed to have perfectly arranged de Broglie wavelengths.

9. Everything as Waves! • Schrödinger found that any particle could be described as a wave. And since any material object consists of particles, the object in turn is really just a wave. • Furthermore, any physical object does not really exist in a single state; it exists as a “wave function,” with characteristics of many states at the same time. • Unlike the idea that particles that sharp, clearly defined edges, we see that particles—close up—are better thought of as just probability distributions. Their edges are fuzzy.

10. A New Way to Think of Matter • Old perspective You can say where a particle in a box is. • New perspective A particle in a box is potentially anywhere in the box. It exists as a “wave function.” Its location is not determined until you measure it. The wave function exists throughout the entire Universe, and it is possible that the particle is anywhere in the Universe. It is the observing of the particle that determines reality, by “collapsing the wave function” into a value.

11. Duality, Multiplicity, Infinitisity • At any moment, you could move to another point in the Universe,even if you couldn’t normally get there! (Ex. Quantum tunneling) • Consider the double electron gun. Which hole does the electron travel through? Top or bottom? • Why choose? Schrödinger says the electron exists in TWO states, one state passes through the top gap, the second passes through the bottom gap. • This works, even if you fire just one electron at a time!

12. A Famous Oddity of Reality • An unmeasured system exists, simultaneously, as a combination of many (even contradictory) states. Hence, Schrödinger’s cat.

13. What Does it Mean to be a Wave? Just as photons reflect and transmit at a glass wall, matter reflects and transmits at potential energy boundaries!

14. Particle-Wave Duality Summary • Particle-wave duality applies to light; • Particle-wave duality applies to matter; • Particle-wave duality applies to you.